The battle over the federal deficit hasn’t flipped in favor of the Democrats. The GOP isn’t suddenly at grave risk of losing its House majority.

But after two years of getting pummeled over spending and the size of government, Democrats now appear to have found a political weapon that’s capable of evening out the fight: Medicare.

The popular entitlement program wasn’t the sole issue behind Kathy Hochul’s upset victory in a New York special election Tuesday night, but strategists in both parties say it was an important force. And for the first time since November, the idea that Democrats might have a shot at winning back the House is no longer a laughing matter.

The three-way race between Hochul, Republican Assemblywoman Jane Corwin and self-funding independent Jack Davis offers at best mixed omens for the 2012 campaign. Hochul drew a stronger-than-expected 47 percent of the vote, and Corwin won an anemic 42 percent. But the 9 percent Davis took as a third-party candidate prevented any candidate from getting a telling majority.

A former Democrat running as a tea party standard bearer, Davis likely skewed the results against the GOP nominee. Yet Hochul wasn’t exactly fighting on even ground, either: Republicans hold a registration edge in the 26th District and John McCain won the area in 2008 by 6 percentage points. She also was outspent by the wealthy Corwin and Republican outside groups.

To Hochul supporters, there was no question what turned the tide of the campaign. At the Democrat’s election night celebration at a UAW hall in Amherst, an elated crowd chanted, “Medicare,” over and over again as Hochul declared victory.

“We had the issues on our side,” Hochul told her supporters, asking rhetorically: “Did we not have the right issues on our side?”

Hochul’s almost single-minded focus on entitlements — Democrat might just dub her the congresswoman from Medicare — accomplished a few key goals: It put her on the right side of seniors. It forced Corwin to fight the election on Democratic-friendly ground. Most of all, it gave Hochul a way of pushing back on the GOP’s popular fiscal conservative message — without losing the independent voters who loathe excessive government spending.

Rather than defending the federal budget, writ large, Hochul cast the debate over spending entirely in terms of one of the most beloved major programs on the books.

By focusing on Medicare, Democrats say, Hochul and other candidates can make a larger argument about Republican priorities and what the GOP is willing to cut in Wisconsin Rep. Paul Ryan’s much-touted budget plan.

“Republicans like to pretend that they are doing something noble, something fair — in the interest of asking all Americans to sacrifice,” said Alixandria Lapp, executive director of the pro-Democratic House Majority PAC, which invested heavily in the race. “They’re not asking oil and gas companies to sacrifice. They’re not asking multimillionaires to sacrifice. Medicare’s going to be a very important part of that overall message and a fundamental referendum for the 2012 election.”

Buffalo Mayor Byron Brown, a Democrat, told POLITICO that Hochul’s win “shows the Democratic message resonates with independents. I do think it changes the debate a bit.”

Republicans blasted out a flurry of statements from party leaders Tuesday night, all rejecting the idea that the debate over entitlements was the decisive factor in the New York race. Instead, the GOP pointed to Davis’s involvement and — privately — groused about Corwin’s unsteadiness on the campaign trail.

But while top Republicans resisted calling the race an up-or-down vote on Medicare, some acknowledged that the GOP had spent the final weeks of the campaign with its back against a wall, having effectively lost control of the campaign narrative.

“They were on defense the whole time on Medicare, not on offense on the deficit or Obamacare or anything else,” said former Virginia Rep. Tom Davis, who chaired the National Republican Congressional Committee. “You can’t just sit there and be a punching bag on this issue, and that’s what they were.”

Former New York Rep. Tom Reynolds, himself a former NRCC chairman who held the 26th District seat until 2009, said Medicare “appears to have had an impact both with seniors and independent voters,” adding: “Anyone who says this is all Medicare either hasn’t watched the race closely or is just spinning.”

“This race has a lot of complexities,” he said, “which include Medicare but also include a $3 million candidate running on the tea party ine.”

One Republican strategist who follows House races put the party’s position in grimmer terms, predicting: “Medicare will define 2012.”

“From Day One, our members need to be attacking their challenger for supporting the president’s Medicare-cutting health care bill and his plan to ration benefits for future seniors,” the strategist wrote in an email. “Paul Ryan was wrong; leaders don’t change polls — scaring seniors changes polls, and we had better be prepared to do it as shamelessly as they did in this special if we want to retain the majority.”

The chance that the GOP could lose 24 seats next year – and with them, control of the House — still seems remote. But unlike a few months ago, it no longer seems like an impossibility.

There are limits, of course, to the predictive value of a single special election, especially one featuring a third-party wild card. Democrats learned that in 2010, after a pair of 2009 upstate New York Democratic victories and a 2010 win in western Pennsylvania failed to forecast the conservative midterm wave.

But a Siena College poll published the weekend before the election appears to confirm that something in the underlying issue debate has changed.

In the survey, the percentage of voters who named Medicare as the top issue in the race (21 percent) was approximately equal to the number who said the deficit was most important (19 percent). Corwin held the kind of advantage among deficit hawks you would expect from a Republican, taking 30 percent to Hochul’s 9 percent.

Among voters who said Medicare was the single most important issue, Hochul held an even greater advantage, outdoing Corwin by a difference of 38 percent to 9 percent.

If Democrats seem to have evened out the playing field, however, the biggest unresolved issue of the budding 2012 campaign remains unresolved. Neither candidate took a clear advantage on the economy, which most analysts believe will tip the balance to one party or the other next year.

In Siena’s polling, the 20 percent of voters who said jobs was the No. 1 issue on their minds split between the major party candidates, giving 17 percent support to each. The independent, trade-protectionist Davis clobbered both Hochul and Corwin among jobs voters, drawing 44 percent from that bloc.

It’s not clear where Davis’s remaining voters would have gone if he had dropped out of the race, though his support bled to both sides as he came under attack on television. It’s possible that one party would have gained a clear advantage or that Hochul and Corwin would have continued to carve up Davis’s bloc in roughly equal parts.

In any case, both parties already were signaling late Tuesday that they recognize Medicare, spending and Ryan’s budget may not be the be-all, end-all of the next campaign.

In a statement congratulating Hochul on her election, President Obama conspicuously refrained from mentioning Medicare or the Ryan budget, which he’s criticized in the past.

Instead, Obama said that he and Hochul “both believe that we need to create jobs, grow our economy and reduce the deficit in order to out-compete other nations and win the future.”

At least some Republicans agree that it’s those terms of debate that will frame the larger 2012 campaign.

“With all the noise aside, the 2012 election will be about jobs and the economy,” said a second Republican strategist, “not about a Wisconsin congressman unknown to anyone outside the Beltway, nor his plan to reform Medicare that has zero chance of making it to the president’s desk.”